1. Technical Field
The present invention relates generally to transient simulators, and more particularly, to a transient simulation system, methods and program product that implement an adaptive piecewise constant model.
2. Related Art
With the continuing miniaturization of very large scale integrated (VLSI) circuitry, interest in conducting formal circuit tuning using circuit transient simulation for gradient calculation is increasing. “Transient simulation” is the analysis of a circuit during time-varying conditions. “Tuning” includes optimization of a number of circuit parameters, e.g., device widths, to maximize circuit performance relative to circuit parameters. A challenge for circuit transient simulation is improving simulator performance, i.e., run time. Tuning also requires conducting another simulation to determine “gradients” for the circuit, which are circuit measurement sensitivities to other circuit parameters, e.g., a transistor's width effect on circuit delay, resistor size effect on circuit speed, etc. This technique further increases the importance of performance. Performance of a simulator is based on how many operations are required to determine circuit performance and gradients. Unfortunately, it is common for a particular simulation operation to be called millions of times during a tuning run.
One common simulation approach tests a circuit design by conducting simulations based on directly solving for voltages and currents via a simultaneous solve technique. Many of these type transient simulators provide for optimization of simulation by allowing an adaptive timing step, with the allowable timing step being chosen to ensure that some user-defined error criteria is satisfied. For example, a local truncation error (LTE) may be implemented that describes a single-step voltage error as a function of the time step. This adaptive timing step is advantageous for two reasons. First, it allows the simulator to adapt its rate of progress as needed to maintain accuracy, while maximizing performance. Second, it allows the user to have some level of control over a performance/accuracy tradeoff. There are some types of event-based fast simulators, however, for which this adaptive timing step capability is not possible.
One type of simulator in which an adaptive timing step is not possible are those that rely on piecewise constant (PWC) table models to represent the simulation parameters. FIG. 1 illustrates a graphical representation of a PWC table model in which a change in current (ΔIR) is constant within the model and a change in voltage (ΔV) is constant for each step within the PWC model. In some cases, a change in current (ΔIR) may vary. PWC table models know current and voltage changes occurring at a particular circuit element at issue, but do not know the timing of the changes. PWC simulators solve for the time to the next step (h), or “segment boundary,” in the PWC model. Once the time solving step is complete, the relevant values are then obtained directly from a PWC table model, i.e., these parameters remain constant between steps by definition. This model is in contrast to the above-described simulators in which a timing change is known and the current and voltage parameter values are simultaneously determined.
Although PWC approximation aids in rapid circuit simulation by limiting all circuit changes to predefined values at discrete points in time, this approach also makes it difficult to balance performance and accuracy available in other simulators because the integration scheme and simulation accuracy are essentially predefined in the PWC table models. That is, the simulation steps are determined solely by the table step size. To ensure accurate simulation with these simulators, the step sizes of the PWC model must be made fine enough to maintain accuracy over the worst case predicted simulation conditions. Unfortunately, this situation typically results in a very conservative level of accuracy for at least a portion of the simulation so as not to lose performance.
While it is possible to affect performance versus accuracy at a crude level in a PWC simulator, for example, through definition of a single optimized table step size during PWC model generation, it is not possible to implement, for example, an LTE relation to provide a controlled performance/accuracy balance. This inefficiency is particularly troublesome given the typical application for a PWC simulation approach—circuit tuning. Despite PWC simulators not providing the most efficient approach for transient simulation, their use remains advantageous because they provide the most efficient means of evaluating sensitivities for non-stiff systems. Unfortunately, as gradients are typically calculated many times inside a particular tuning loop, the effect on performance of a PWC simulation is significant.
In view of the foregoing, there is a need in the art for way of improving simulation performance for a PWC-based transient simulator.